Understanding protein folding cooperativity based on topological consideration

The folding cooperativity is an important issue of protein folding dynamics. Since the native topology plays a significant role in determining the folding behavior of proteins, we believe that it also has close relationship with the folding cooperativity. In the present work, we perform simulations on proteins Naf-BBL, QNND-BBL, CI2, and SH3 with the Gomacr model and compare their different folding behaviors. By analyzing the weak cooperative folding of protein Naf-BBL in detail, we found that the folding of Naf-BBL shows relatively weak thermodynamic coupling between residues, and such weak coupling is found mainly between the nonlocal native contacts. This finding complements our understandings on the source of barrierless folding of Naf-BBL and promotes us to analyze the topological origins of the poor thermodynamic coupling of Naf-BBL. Then, we further extend our analysis to other two-state and multistate proteins. Based on the considerations of the thermodynamic coupling and kinetic coupling, we conclude that the fraction of scattered native contacts, the difference in loop entropy of contacts, and the long range relative contact order are the major topological factors that influence the folding cooperativity. The combination of these three tertiary structural features shows significant correlations with the folding types of proteins. Moreover, we also discuss the topological factors related to downhill folding. Finally, the generic role of tertiary structure in determining the folding cooperativity is summarized.